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    Abstract—This paper presents optimal model-based control of a heating, ventilating, and air-conditioning (HVAC) system.This HVAC system is made of two heat exchangers: an air-to-air heat exchanger (a rotary wheel heat recovery) and a water-to-air heat exchanger. First dynamic model of the HVAC system is developed. Then the optimal control structure is designed and implemented. The HVAC system is splitted into two subsystems.By selecting the right set-points and appropriate cost functions for each subsystem controller the optimal control strategy is respected to gaurantee the minimum thermal and electrical energy consumption. Finally, the controller is applied to control the mentioned HVAC system and the results show that the expected goals are fulfilled.24317
    I. INTRODUCTION
    The consumption of energy by heating, ventilating, and
    air conditioning (HVAC) equipment in industrial and com-
    mercial buildings constitutes a great part of the world energy
    consumption [1]. In spite of the advancements made in mi-
    croprocessor technology and its impact on the development
    of new control methodologies for HVAC systems aiming at
    improving their energy efficiency, the process of operating
    HVAC equipment in commercial and industrial buildings is
    still an inefficient and high-energy consumption process.
    It has been estimated that by optimal control of HVAC
    systems almost 100 GWh energy can be saved yearly in
    Denmark (five million inhabitants) [2]. It shows that a huge
    amount of energy can be saved and according to the current
    energy prices it will be reasonable to invest a little bit more
    in the first cost of HVAC systems.
    In this paper, an integrated control system is developed.
    That is, in the proposed control system there is no need for
    an expilicit supervisory layer to make the system work in
    its optimal conditions. The optimal control strategy that has
    been developed in [2] is implemented here. So, the controller
    follows the optimal control strategy while it tracks the set-
    point. In Section II, the dynamic model of the HVAC system
    is described. The controller design is presented in Section III.
    Finally, the results of applying the proposed control system
    is shown in Section IV.
    Mohammad Komareji is a PhD student in The Department of Control and
    Automation, Institute of Electronic Systems, Aalborg University, Aalborg,
    Denmark; komareji@control.aau.dk
    Jakob Stoustrup is with Aalborg University as a Professsor in The
    Department of Control and Automation; jakob@control.aau.dk
    Henrik Rasmussen is with Aalborg University as an Associate Professor
    in The Department of Control and Automation; hr@control.aau.dk
    Niels Bidstrup is with Grundfos Management A/S as a Chief Engineer,
    Ph.D.; nbidstrup@grundfos.com
    Peter Svendsen is with Danish Technological Institute (DTI) as a Project
    Manager; Peter.Svendsen@teknologisk.dk
    Finn Nielsen is with Exhausto A/S as a Project Manager;
    FNI@exhausto.dk
    TABLE I
    NOMENCLATURE
    qa inlet or outlet air flow (m3=h)
    TE21 outdoor air temperature (
    oC)
    TE22 temperature of outdoor air after heat recovery (
    oC)
    TE11 room air temperature (
    oC)
    TE12 temperature of room air after heat recovery (
    oC)
    qwt water flow of the tertiary circuit (l=h)
    qws water flow of the supply (primary/secondary) circuit (l=h)
    Twin tertiary supply water temperature (
    oC)
    Twout tertiary return water temperature (
    oC)
    Tinlet temperature of the supply air (
    oC)
    T pin primary/secondary supply water temperature (
    oC)
    T pout primary/secondary return water temperature (
    oC)
    ht2 air-to-air heat exchanger temperature efficiency
    (ht2 = TE22 TE21
    TE11 TE21 )
    rw water mass density (Kg=m3)
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